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A298262 Number of integer partitions of n using relatively prime non-divisors of n. 1
0, 0, 0, 0, 1, 0, 3, 1, 3, 2, 13, 1, 23, 7, 10, 8, 65, 5, 104, 11, 53, 53, 252, 8, 244, 124, 203, 67, 846, 22, 1237, 157, 636, 569, 1074, 51, 3659, 1140, 1827, 221, 7244, 236, 10086, 1162, 1844, 4169, 19195, 225, 17657, 2997 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{d|n} mu(n/d) * A098743(d).

EXAMPLE

The a(11) = 13 partitions: (65), (74), (83), (92), (443), (533), (542), (632), (722), (3332), (4322), (5222), (32222).

The a(14) = 7 partitions: (9 5), (11 3), (5 5 4), (6 5 3), (8 3 3), (4 4 3 3), (5 3 3 3).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And[GCD@@#===1, !Or@@(Divisible[n, #]&/@#)]&]], {n, 50}]

PROG

(PARI) \\ here b(n) is A098743.

b(n)={polcoef(1/prod(k=1, n, if(n%k, 1 - x^k, 1) + O(x*x^n)), n)}

a(n)={sumdiv(n, d, moebius(d)*b(n/d))} \\ Andrew Howroyd, Aug 29 2018

CROSSREFS

Cf. A000041, A000837, A002577, A002865, A018818, A018819, A049820, A098743, A100953, A200745, A275870, A281116.

Sequence in context: A112164 A300580 A075676 * A124814 A122567 A122431

Adjacent sequences:  A298259 A298260 A298261 * A298263 A298264 A298265

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 15 2018

STATUS

approved

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Last modified June 24 17:51 EDT 2021. Contains 345419 sequences. (Running on oeis4.)